The present invention relates to the continuous production of foamed and cured synthetic resin sheets that may be usable for sheet insulation, prefabricated walls, mattresses, packing material, or many other uses wherein a foam resin, either rigid or resilient, is desired. Covered sheets of paper, particularly Kraft paper, are used to protect the side dams and endless conveyors of the molding tunnel from contact with the resin during its foaming and curing, and in such conventional devices there is the problem that with clamping of the paper so as to prevent leakage past the paper, such clamping is accomplished before the foaming process is ended so that there will be either excess paper within the molding tunnel to produce wrinkles or insufficient paper within the molding tunnel to produce rounded corners, and if clamping is delayed there can be considerable leakage to foul the apparatus.